Computer Science > Computer Vision and Pattern Recognition

Title:
What's In A Patch, II: Visualizing generic surfaces

Abstract: We continue the development of a linear algebraic framework for the
shape-from-shading problem, exploiting the manner in which tensors arise when
scalar (e.g. image) and vector (e.g. surface normal) fields are differentiated
multiple times. In this paper we apply that framework to develop Taylor
expansions of the normal field and build a boot-strapping algorithm to find
these polynomial surface solutions (under any light source) consistent with a
given patch to arbitrary order. A generic constraint on the image derivatives
restricts these solutions to a 2-D subspace, plus an unknown rotation matrix.
The parameters for the subspace and rotation matrix encapsulate the ambiguity
in the shading problem.